Estimating the mean and standard deviation of concentration distributions using censored samples

Environmental data sets of pollutant concentrations in air, water, and soil frequently include unquantified sample values reported only as being below the analytical method detection limit. These values, referred to as censored values, should be considered in the estimation of distribution parameters as each represents some value of pollutant concentration between zero and the detection limit. Most of the currently accepted methods for estimating the population parameters of environmental data sets containing censored values rely upon the assumption of an underlying normal (or transformed normal) distribution. This assumption can result in unacceptable levels of error in parameter estimation due to the unbounded left tail of the normal distribution. With the beta distribution, which is bounded by the same range of a distribution of concentrations, $\rm\lbrack0\le x\le1\rbrack,$ parameter estimation errors resulting from improper distribution bounds are avoided. This work developed a method that uses the beta distribution to estimate population parameters from censored environmental data sets and evaluated its performance in comparison to currently accepted methods that rely upon an underlying normal (or transformed normal) distribution. Data sets were generated assuming typical values encountered in environmental pollutant evaluation for mean, standard deviation, and number of variates. For each set of model values, data sets were generated assuming that the data was distributed either normally, lognormally, or according to a beta distribution. For varying levels of censoring, two established methods of parameter estimation, regression on normal ordered statistics, and regression on lognormal ordered statistics, were used to estimate the known mean and standard deviation of each data set. The method developed for this study, employing a beta distribution assumption, was also used to estimate parameters and the relative accuracy of all three methods were compared. For data sets of all three distribution types, and for censoring levels up to 50%, the performance of the new method equaled, if not exceeded, the performance of the two established methods. Because of its robustness in parameter estimation regardless of distribution type or censoring level, the method employing the beta distribution should be considered for full development in estimating parameters for censored environmental data sets. ^

Qualitative behaviour of L1 and L2 standard deviation in insulations measurements according to standard UNE EN ISO 140-4

Knowledge of the uncertainty of measurement of testing results is important when results have to be compared with limits and specifications. In the measurement of sound insulation following standards UNE EN ISO 140-4 the uncertainty of the final magnitude is mainly associated to the average sound pressure levels L1 and L2 measured. A parameter that allows us to quantify the spatial variation of the sound pressure level is the standard deviation of the pressure levels measured at different points of the room. In this work, for a wide number of measurements following standards UNE EN ISO 140-4 we analyzed qualitatively the behaviour of the standard deviation for L1 and L2. The study of sound fields in enclosed spaces is very difficult. There are a wide variety of rooms with different sound fields depending on factors as volume, geometry and materials. In general, we observe that the L1 and L2 standard deviations contain peaks and dips independent on characteristics of the rooms at single frequencies that could correspond to critical frequencies of walls, floors and windows or even to temporal alterations of the sound field. Also, in most measurements according to UNE EN ISO 140-4 a large similitude between L1 and L2 standard deviation is found. We believe that such result points to a coupled system between source and receiving rooms, mainly at low frequencies the shape of the L1 and L2 standard deviations is comparable to the velocity level standard deviation on a wall

Tables describing small-sample properties of the mean, median, standard deviation, and other statistics in sampling from various distributions /

Mode of access: Internet.

Standard Values for Real-Time Transthoracic Three-Dimensional Echocardiographic Dyssynchrony Indexes in a Normal Population

Background: There is a paucity of information describing the real-time 3-dimensional echocardiography (RT3DE) and dyssynchrony indexes (DIs) of a normal population. We evaluate the RT3DE DIs in a population with normal electrocardiograms and 2- and 3-dimensional echocardiographic analyses. This information is relevant for cardiac resynchronization therapy. Methods: We evaluated 131 healthy volunteers (73 were male, aged 46 +/- 14 years) who were referred for routine echocardiography; who presented normal cardiac structure on electrocardiography, 2-dimensional echocardiography, and RT3DE; and who had no history of cardiac diseases. We analyzed 3-dimensional left ventricular ejection fraction, left ventricle end-diastolic volume, left ventricle end-systolic volume, and left ventricular systolic DI% (6-, 12-, and 16-segment models). RT3DE data were analyzed by quantifying the statistical distribution (mean, median, standard deviation [SD], relative SD, coefficient of skewness, coefficient of kurtosis, Kolmogorov-Smirnov test, D`Agostino-Pearson test, percentiles, and 95% confidence interval). Results: Left ventricular ejection fraction ranged from 50% to 80% (66.1% +/- 7.1%); left ventricle end-diastolic volume ranged from 39.8 to 145 mL (79.1 +/- 24.9 mL); left ventricle end-systolic volume ranged from 12.9 to 66 mL (27 +/- 12.1 mL); 6-segment DI% ranged from 0.20% to 3.80% (1.21% +/- 0.66%), median: 1.06, relative SD: 0.5482, coefficient of skewness: 1.2620 (P < .0001), coefficient of Kurtosis: 1.9956 (P = .0039); percentile 2.5%: 0.2900, percentile 97.5%: 2.8300; 12-segment DI% ranged from 0.22% to 4.01% (1.29% +/- 0.71%), median: 1.14, relative SD: 0.95, coefficient of skewness: 1.1089 (P < .0001), coefficient of Kurtosis: 1.6372 (P = .0100), percentile 2.5%: 0.2850, percentile 97.5%: 3.0700; and 16-segment DI% ranged from 0.29% to 4.88% (1.59 +/- 0.99), median: 1.39, relative SD: 0.56, coefficient of skewness: 1.0792 (P < .0001), coefficient of Kurtosis: 0.9248 (P = .07), percentile 2.5%: 0.3750, percentile 97.5%: 3.750. Conclusion: This study allows for the quantification of RT3DE DIs in normal subjects, providing a comparison for patients with heart failure who may be candidates for cardiac resynchronization therapy. (J Am Soc Echocardiogr 2008; 21: 1229-1235)

Electrothermal AAS determination of Ni in soft drinks using Co as the internal standard

A method for the direct determination of Ni in soft drinks by graphite furnace atomic absorption spectrometry using a transversely heated graphite atomizer (THGA), Zeeman-effect background corrector, and Co as the internal standard (IS) is proposed. Magnesium nitrate was used to stabilize both Ni and Co. All diluted samples (1+1) in 0.2% (v/v) HNO3 and reference solutions [5.0-50 mu g L-1 Ni in 0.2% (v/v) HNO3] were spiked with 50 mu g L-1 Co. For a 20-mu L sample dispensed into the atomizer, correlations between the ratio of absorbance of Ni to absorbance of Co and the analyte concentration were close to 0.9996. The relative standard deviation of the measurements varied from 0.5 to 3.4% and 1.0 to 7.0% (n=12) with and without IS, respectively. Recoveries within 98-104% for Ni spikes were obtained using IS. The characteristic mass was calculated as 43 pg Ni and the limit of detection was 1.4 mu g L-1. The accuracy of the method was checked for the direct determination of Ni in soft drinks and the results obtained with IS were better than those without IS.

Evaluation of Bi as internal standard to minimize matrix effects on the direct determination of Pb in vinegar by graphite furnace atomic absorption spectrometry using Ru permanent modifier with co-injection of Pd/Mg(NO3)(2)

Bismuth was evaluated as an internal standard for the direct determination of Pb in vinegar by graphite furnace atomic absorption spectrometry using Ru as a permanent modifier with co-injection of Pd/Mg(NO3)(2). The correlation coefficient of the graph plotted from the non-nalized absorbance signals of Bi versus Pb was r=0.989. Matrix effects were evaluated by analyzing the slope ratios between the analytical curve, and analytical curves obtained from Pb additions in red and white wine vinegar obtained from reference solutions prepared in 0.2% (v/v) HNO3, samples. The calculated ratios were around 1.04 and 1.02 for analytical curves established applying an internal standard and 1.3 and 1.5 for analvtical curves without. Analytical curves in the 2.5-15 pg L-1 Pb concentration interval were established using the ratio Pb absorbance to Bi absorbance versus analvte concentration, and typical linear correlations of r=0.999 were obtained. The proposed method was applied for direct determination of Pb in 18 commercial vinegar samples and the Pb concentration varied from 2.6 to 31 pg L-1. Results were in agreement at a 95% confidence level (paired t-test) with those obtained for digested samples. Recoveries of Pb added to vinegars varied from 96 to 108% with and from 72 to 86% without an internal standard. Two water standard reference materials diluted in vinegar sample were also analyzed and results were in agreement with certified values at a 95% confidence level. The characteristic mass was 40 pg Pb and the useful lifetime of the tube was around 1600 firings. The limit of detection was 0.3 mu g L-1 and the relative standard deviation was <= 3.8% and <= 8.3% (n = 12) for a sample containing, 10 mu L-1 Pb with and without internal standard, respectively. (C) 2007 Elsevier B.V. All rights reserved.